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The Three-Dimensional Decomposition of Volatility Memory

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  • Ziyao Wang
  • A. Alexandre Trindade
  • Svetlozar T. Rachev

Abstract

This paper develops a three-dimensional decomposition of volatility memory into orthogonal components of level, shape, and tempo. The framework unifies regime-switching, fractional-integration, and business-time approaches within a single canonical representation that identifies how each dimension governs persistence strength, long-memory form, and temporal speed. We establish conditions for existence, uniqueness, and ergodicity of this decomposition and show that all GARCH-type processes arise as special cases. Empirically, applications to SPY and EURUSD (2005--2024) reveal that volatility memory is state-dependent: regime and tempo gates dominate in equities, while fractional-memory gates prevail in foreign exchange. The unified tri-gate model jointly captures these effects. By formalizing volatility dynamics through a level--shape--tempo structure, the paper provides a coherent link between information flow, market activity, and the evolving memory of financial volatility.

Suggested Citation

  • Ziyao Wang & A. Alexandre Trindade & Svetlozar T. Rachev, 2025. "The Three-Dimensional Decomposition of Volatility Memory," Papers 2512.02166, arXiv.org.
    • Handle: RePEc:arx:papers:2512.02166
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    File URL: http://arxiv.org/pdf/2512.02166
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